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Fig. 1.12.
Left Euler-Lagrange tensor,
K
1
>
0
,K
2
>
0, left Euler-Lagrange circle
S
1
, left Euler-Lagrange
ellipse
E
1
√
K
1
,
√
K
2
S
1
, left Euler-Lagrange
Fig. 1.13.
Left Euler-Lagrange tensor,
K
1
>
0
,K
2
<
0, left Euler-Lagrange circle
H
1
√
K
1
,
√
K
2
hyperbola
, left and right focal points
F
l
and
F
r
Fig. 1.14.
Right Euler-Lagrange tensor,
κ
1
>
0
,κ
2
>
0, right Euler-Lagrange circle
S
1
, right Euler-Lagrange
E
1
√
K
1
,
√
K
2
ellipse
Corollary 1.9 (Relation between the Cauchy-Green and the Euler-Lagrange deformation tensor).
2E
l
=J
l
G
r
J
l
J
r
G
l
J
r
=G
r
−
G
l
=C
l
−
G
l
2E
r
=G
r
−
−
C
r
versus
versus
versus
C
l
=2E
l
+G
l
,
C
r
=G
r
−
2E
r
;
(1.120)
E
l
=J
l
E
r
J
l
versus E
r
=J
r
E
l
J
r
;
2
K
i
=
Λ
i
∀i
=1
,
2
versus 2
κ
i
=
λ
i
−
1
∀i
=1
,
2
.
End of Corollary.
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